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Question

xcosα=ycos(α2π3)=zcos(α+2π3)
then x + y + z is equal to

A
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B
0
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C
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D
14cos3α
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Solution

The correct option is B 0

Let xcosα=ycos(α2π3)=ycos(α+2π3)=k

Now, x=kcosα
y=kcos(α2π3)
z=kcos(α+2π3)

Now, x+y+z=kcosα+kcos(α2π3)+kcos(α+2π3)
x+y+z=kcosα+kcosαcos2π3+ksinαsin2π3+kcosαcos2π3ksinαsin2π3
x+y+z=kcosα+2kcosαcos2π3
x+y+z=kcosα+2kcosα(12)
Hence, x+y+z=0


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